2017 Volume 9 Issue 1 Pages 1-6
This paper considers a multi-objective bottleneck transportation problem with fuzzy random constraint about transportation time and chance constraint about the total cost. There exist m supply points with flexible supply quantity and n demand points with flexible demand quantity. For each route, that is, each pair of a supply and a demand, the transportation time is an independent random variable according to a normal distribution with an uncertain mean denoted by an L-fuzzy number and a crisp variance. Further for each route, existence possibility denoting the preference choosing the route is attached. Satisfaction degrees about the supply and demand quantity are attached to each supply and demand point, respectively. These satisfaction degrees are denoted by membership functions of corresponding fuzzy sets. Moreover transportation cost on each route is a random variable and these random variables are assumed to be independent each other. We consider four criteria, given as follows. (1) Minimize the transportation time target under the possibility that the satisfaction probability with respect to transportation time below the target is over a certain thresh-hold should be over a given level. (2) Maximize the minimal preference among used routes in transportation. (3) Maximize the minimal satisfaction degree among all supply and demand points. (4) Minimizing the budget under the chance constraint, the probability that the total cost is below the budget should be over a certain level. Above setting, we formulate the model with three objective and fuzzy random constraint with respect to random transportation time of each route. This is a multi-objective bottleneck transportation problem. First this problem is transformed into deterministic equivalent problem with four objectives. Usually an optimal transportation pattern optimizing four objectives at a time and so we propose solution algorithm to seek some non-dominated transportation pattern after non-domination with introducing threshold about preference of route. Finally, we summarize the result of the paper and discuss future research problems.
